Models for count data with an application to Healthy Days measures: are you driving in screws with a hammer?

Count data are often collected in chronic disease research, and sometimes these data have a skewed distribution. The number of unhealthy days reported in the Behavioral Risk Factor Surveillance System (BRFSS) is an example of such data: most respondents report zero days. Studies have either categorized the Healthy Days measure or used linear regression models. We used alternative regression models for these count data and examined the effect on statistical inference.

Using responses from participants aged 35 years or older from 12 states that included a homeownership question in their 2009 BRFSS, we compared 5 multivariate regression models--logistic, linear, Poisson, negative binomial, and zero-inflated negative binomial--with respect to 1) how well the modeled data fit the observed data and 2) how model selections affect inferences.

Most respondents (66.8%) reported zero mentally unhealthy days. The distribution was highly skewed (variance = 58.7, mean = 3.3 d). Zero-inflated negative binomial regression provided the best-fitting model, followed by negative binomial regression. A significant independent association between homeownership and number of mentally unhealthy days was not found in the logistic, linear, or Poisson regression model but was found in the negative binomial model. The zero-inflated negative binomial model showed that homeowners were 24% more likely than nonowners to have excess zero mentally unhealthy days (adjusted odds ratio, 1.24; 95% confidence interval, 1.08-1.43), but it did not show an association between homeownership and the number of unhealthy days.

Our comparison of regression models indicates the importance of examining data distribution and selecting models with appropriate assumptions. Otherwise, statistical inferences might be misleading.